Matrix models and N=2 gauge theory

We describe how the ingredients and results of the Seiberg-Witten solution to N=2 supersymmetric U(N) gauge theory may be obtained from a matrix model.Comment: 6 pages, AMSLaTeX (ws-procs9x6.cls included). Presented at QTS3 (Cincinnati, Ohio, Sept. 10-14, 2003

Wilson line approach to gravity in the high energy limit

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories.Comment: 33 pages, 5 figure

Electroweak strings and fermions

Z-strings in the Weinberg-Salam model including fermions are unstable for all values of the parameters. The cause of this instability is the fermion vacuum energy in the Z-string background. Z-strings with non-zero fermion densities, however, may still be stable

Analytical Representation of a Black Hole Puncture Solution

The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture simulations, the evolution of a single black hole leads to a well-known time-independent, maximal slicing of Schwarzschild. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example for testing and calibrating numerical codes that employ moving puncture techniques. In this Brief Report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes

Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation

We use matrix model technology to study the N=2 U(N) gauge theory with N_f massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods a_i and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve from the large-M solution of the matrix model. We show that the two cases N_f<N and N \le N_f < 2N can be treated simultaneously

Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes

The IR divergences of supergravity amplitudes are less severe than those of planar SYM amplitudes, and are comparable to those subleading-color SYM amplitudes that are most subleading in the 1/N expansion, namely O(1/epsilon^L) for L-loop amplitudes. We derive linear relations between one- and two-loop four-point amplitudes and one-loop five-point amplitudes of N = 4, 5, and 6 supergravity and the most-subleading-color contributions of the analogous amplitudes of N = 0, 1, and 2 SYM theory, extending earlier results for N = 8 supergravity amplitudes. Our work relies on linear relations between N >= 4 supergravity and planar SYM amplitudes that were recently derived using the double-copy property of gravity, and color-kinematic duality of gauge theories.Comment: 21 pages, 1 figur

The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N=2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a_i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-Witten differential or curve. We also compute the N=2 prepotential F(a) perturbatively up to the first-instanton level finding agreement with the known result